- #1
octol
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I've been banging my head against this problem for some time now, and I just can't solve it. The problem seems fairly simple, but for some reason I don't get it.
Given the coordinate transformation matrix
[tex]A=\left( \begin{array}{ccc}\cos{\alpha}&0&-\sin{\alpha}\\0&1&0\\\sin{\alpha}&0&\cos{\alpha}\end{array}\right)[/tex]
show how
[tex]\mathbf{B}=\mathbf{r} \times \hat{z}[/tex]
transforms. Now how do I do this? For example, I've tried writing out the cross product, which becomes
[tex]\mathbf{B} = -y\hat{x} + x\hat{y}[/tex]
and then simply transforming this vector using the above matrix A, but it doesn't seem to work.
Any hints on how to think about this?
Given the coordinate transformation matrix
[tex]A=\left( \begin{array}{ccc}\cos{\alpha}&0&-\sin{\alpha}\\0&1&0\\\sin{\alpha}&0&\cos{\alpha}\end{array}\right)[/tex]
show how
[tex]\mathbf{B}=\mathbf{r} \times \hat{z}[/tex]
transforms. Now how do I do this? For example, I've tried writing out the cross product, which becomes
[tex]\mathbf{B} = -y\hat{x} + x\hat{y}[/tex]
and then simply transforming this vector using the above matrix A, but it doesn't seem to work.
Any hints on how to think about this?
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